Question 1

Probability calculator
Distribution: Log normal
Mean log    : 0 
St. dev log : 1 
Lower bound : 0 
Upper bound : 1 

P(X < 0) = 0
P(X > 0) = 1
P(X < 1) = 0.5
P(X > 1) = 0.5
P(0 < X < 1)     = 0.5
1 - P(0 < X < 1) = 0.5


What is the probability that a log-normal random variable [in R, lnorm is the noun] whose logarithm has mean equal to 0 and standard deviation equal to 1, takes values less than 1?

0.5

Question 2

Probability calculator
Distribution: Log normal
Mean log    : 0 
St. dev log : 1 
Lower bound : 0 
Upper bound : 0.95 

P(X < 0) = 0
P(X > 0) = 1
P(X < 5.18) = 0.95
P(X > 5.18) = 0.05
P(0 < X < 5.18)     = 0.95
1 - P(0 < X < 5.18) = 0.05


What is the value of a log-normal random variable [in R, lnorm is the noun] whose logarithm has mean equal to 0 and standard deviation equal to 1, such that 0.95 of the probability is below said value?

5.18

Question 3


Plot a random sample of 1000 random draws from the aforementioned lognormal distribution (mean 0 and std. dev. 1).

The purpose is to have you visualize the distribution as a sanity check for 1 and 2.

Question 4

Probability calculator
Distribution: Normal
Mean        : 0 
St. dev     : 1 
Lower bound : 0.15865 
Upper bound : 0.84135 

P(X < -1) = 0.15865
P(X > -1) = 0.841
P(X < 1) = 0.84135
P(X > 1) = 0.159
P(-1 < X < 1)     = 0.6827
1 - P(-1 < X < 1) = 0.317


The central probability in a standard normal distribution between -1 and 1 is 0.6827.

** Figure out z such that the probability between XXX and XXX is 0.6827. The middle of a z (normal 0, 1) is 0 so the probability below 0 is the same as the probability above zero which is 0.5. Now we need 0.6827 to each side. First, split it into two parts. There will be 0.6827/2 on each side of zero. So the first value must then be the solution to 0.5 - 0.34135 or 0.15865: -1. The second value will be 0.5 + 0.34135 or 0.84135: 1.**

Newspapers


Two key features are of note:

  1. The average price is clearly lower at Henry Hub
  2. The amount of variation at Henry Hub is considerably larger than at Tianjin in spite of the fact that the average is lower.

Newspapers: Summary

Data summary
Name Newspapers
Number of rows 61
Number of columns 7
_______________________
Column type frequency:
factor 1
numeric 3
POSIXct 3
________________________
Group variables None

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
Location 0 1 FALSE 2 Hen: 36, Tia: 25

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
Price 0 1.00 3.88 0.15 3.52 3.77 3.92 4.00 4.07 ▂▃▃▅▇
HHPrice 25 0.59 3.80 0.14 3.52 3.69 3.80 3.90 4.07 ▃▆▇▆▃
TianjinPrice 36 0.41 3.99 0.05 3.88 3.98 4.00 4.04 4.05 ▂▂▂▇▇

Variable type: POSIXct

skim_variable n_missing complete_rate min max median n_unique
Date 0 1.00 2013-05-04 2013-10-30 2013-08-06 00:00:00 61
HHDate 25 0.59 2013-05-04 2013-10-25 2013-07-29 12:00:00 36
TianjinDate 36 0.41 2013-05-05 2013-10-30 2013-08-13 00:00:00 25

Two key features are of note:

  1. The average price is clearly lower at Henry Hub
  2. The amount of variation at Henry Hub is considerably larger than at Tianjin in spite of the fact that the average is lower.

Experts


Almost everything that we wish to know can be discerned from this.

  1. Because we can see 100 on the y-axis, we can get a sense of the missing responses; there are far more for Tianjin than Henry Hub.
  2. Experts clearly favor Henry Hub; the split in Build/No is nearly even for Tianjin but overwhelmingly favors Build for Henry Hub.

Experts: Tables

The Raw Table

 Location Build No Total
 HenryHub    66 15    81
  Tianjin    31 33    64
    Total    97 48   145

A Percentage Table

 Location     Build        No
 HenryHub 0.8148148 0.1851852
  Tianjin 0.4843750 0.5156250

  1. Henry Hub has far more responses and more favorable responses than Tianjin.
  2. Experts clearly favor Henry Hub; the split in Build/No is nearly even for Tianjin but overwhelmingly favors Build for Henry Hub.

Forecast


Two things are of note:
1. The data are paired by period; that is the point of the calibration exercise.
2. Henry Hub is almost always forecast higher than Tianjin. Choose a period and you can hover over the associated values to convince yourself of this. Compare the two forecasts for any given period; they are almost always higher for Henry Hub.

Forecast: Data


Henry Hub is almost always forecast higher than Tianjin. The difference column captures this perfectly and shows that it always favors Henry Hub.